Basic Math Examples

$1.11 \cdot 10^{11} = \frac{1000 \cdot 4}{F (3.14 \cdot 10^{- 6})}$

Step 1

Rewrite the equation as $\frac{1000 \cdot 4}{F \cdot 3.14 \cdot 10^{- 6}} = 1.11 \cdot 10^{11}$ .

$\frac{1000 \cdot 4}{F \cdot 3.14 \cdot 10^{- 6}} = 1.11 \cdot 10^{11}$

Step 2

Simplify $\frac{1000 \cdot 4}{F \cdot 3.14 \cdot 10^{- 6}}$ .

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Step 2.1

Move $10^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{1000 \cdot 4 \cdot 10^{6}}{F \cdot 3.14} = 1.11 \cdot 10^{11}$

Step 2.2

Multiply $1000$ by $4$ .

$\frac{4000 \cdot 10^{6}}{F \cdot 3.14} = 1.11 \cdot 10^{11}$

Step 2.3

Move $3.14$ to the left of $F$ .

$\frac{4000 \cdot 10^{6}}{3.14 \cdot F} = 1.11 \cdot 10^{11}$

Step 2.4

Multiply by $1$ .

$\frac{14000 \cdot 10^{6}}{3.14 \cdot F} = 1.11 \cdot 10^{11}$

Step 2.5

Factor $3.14$ out of $3.14 \cdot F$ .

$\frac{14000 \cdot 10^{6}}{3.14 (F)} = 1.11 \cdot 10^{11}$

Step 2.6

Separate fractions.

$\frac{1}{3.14} \cdot \frac{4000 \cdot 10^{6}}{F} = 1.11 \cdot 10^{11}$

Step 2.7

Divide $1$ by $3.14$ .

$0.31847133 \frac{4000 \cdot 10^{6}}{F} = 1.11 \cdot 10^{11}$

Step 2.8

Multiply $0.31847133 \frac{4000 \cdot 10^{6}}{F}$ .

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Step 2.8.1

Combine $0.31847133$ and $\frac{4000 \cdot 10^{6}}{F}$ .

$\frac{0.31847133 \cdot 4000 \cdot 10^{6}}{F} = 1.11 \cdot 10^{11}$

Step 2.8.2

Multiply $4000$ by $0.31847133$ .

$\frac{1273.88535031 \cdot 10^{6}}{F} = 1.11 \cdot 10^{11}$

Step 2.9

Move the decimal point in $1273.88535031$ to the left by $3$ places and increase the power of $10^{6}$ by $3$ .

$\frac{1.27388535 \cdot 10^{9}}{F} = 1.11 \cdot 10^{11}$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$F, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$F$

Step 4

Multiply each term in $\frac{1.27388535 \cdot 10^{9}}{F} = 1.11 \cdot 10^{11}$ by $F$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{1.27388535 \cdot 10^{9}}{F} = 1.11 \cdot 10^{11}$ by $F$ .

$\frac{1.27388535 \cdot 10^{9}}{F} F = 1.11 \cdot 10^{11} F$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $F$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{1.27388535 \cdot 10^{9}}{F} F = 1.11 \cdot 10^{11} F$

Step 4.2.1.2

Rewrite the expression.

$1.27388535 \cdot 10^{9} = 1.11 \cdot 10^{11} F$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $1.11 \cdot 10^{11} F = 1.27388535 \cdot 10^{9}$ .

$1.11 \cdot 10^{11} F = 1.27388535 \cdot 10^{9}$

Step 5.2

Divide each term in $1.11 \cdot 10^{11} F = 1.27388535 \cdot 10^{9}$ by $1.11 \cdot 10^{11}$ and simplify.

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Step 5.2.1

Divide each term in $1.11 \cdot 10^{11} F = 1.27388535 \cdot 10^{9}$ by $1.11 \cdot 10^{11}$ .

$\frac{1.11 \cdot 10^{11} F}{1.11 \cdot 10^{11}} = \frac{1.27388535 \cdot 10^{9}}{1.11 \cdot 10^{11}}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $1.11$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{1.11 \cdot 10^{11} F}{1.11 \cdot 10^{11}} = \frac{1.27388535 \cdot 10^{9}}{1.11 \cdot 10^{11}}$

Step 5.2.2.1.2

Rewrite the expression.

$\frac{10^{11} F}{10^{11}} = \frac{1.27388535 \cdot 10^{9}}{1.11 \cdot 10^{11}}$

Step 5.2.2.2

Cancel the common factor of $10^{11}$ .

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Step 5.2.2.2.1

Cancel the common factor.

$\frac{10^{11} F}{10^{11}} = \frac{1.27388535 \cdot 10^{9}}{1.11 \cdot 10^{11}}$

Step 5.2.2.2.2

Divide $F$ by $1$ .

$F = \frac{1.27388535 \cdot 10^{9}}{1.11 \cdot 10^{11}}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide using scientific notation.

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Step 5.2.3.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$F = (\frac{1.27388535}{1.11}) (\frac{10^{9}}{10^{11}})$

Step 5.2.3.1.2

Divide $1.27388535$ by $1.11$ .

$F = 1.14764445 \frac{10^{9}}{10^{11}}$

Step 5.2.3.1.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$F = 1.14764445 \cdot 10^{9 + 11 \cdot - 1}$

Step 5.2.3.1.4

Multiply $11$ by $- 1$ .

$F = 1.14764445 \cdot 10^{9 - 11}$

Step 5.2.3.1.5

Subtract $11$ from $9$ .

$F = 1.14764445 \cdot 10^{- 2}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$F = 1.14764445 \cdot 10^{- 2}$

Expanded Form:

$F = 0.01147644$